基于可拓域变化代价最小的最优粒度选择

doi:10.6040/j.issn.1671-9352.0.2020.236

摘要/Abstract

摘要： 针对当前最优粒度选择算法对决策域动态变化带来的代价鲜有涉及的问题,引入可拓集方法,结合三支决策思想提出基于可拓域变化代价最小的最优粒度选择模型。首先由可拓评价法确定指标等级离散化数据表,以权重为粒子实施粒化,利用二元关系交算子构建粒层空间;其次融合三支决策划分三个域,基于三个域的动态变化确定可拓集的五个域;然后研究可拓域变化的度量方式,构建代价矩阵,由可拓域变化代价最小确定最优粒层。该模型综合考虑静态和动态特征,为最优粒度选择提供新的途径。最后以黑龙江省水资源承载力数据为例,验证模型的有效性。利用分类与回归树(classification and regression trees, CART)进行灵敏度分析。结果表明模型具有较好的可推广性。

关键词: 粒度选择, 三支决策, 可拓集, 变化代价矩阵, 水资源承载力

Abstract: Aiming at the problem that the cost of dynamic change of decision domain is seldom involved in the current optimal granularity selection algorithm, the extension set method is introduced, and the optimal granularity selection model based on the minimum cost of change of extension domain is proposed by combining the three-way decision. Firstly, the index grade discretization data table is determined by extension evaluation method, and the weight is used as the particle to carry out granulation, and the granular space is constructed by using binary relation crossover operator. Secondly, three domains are divided by fusing three decisions, and five domains of extension set are determined based on the dynamic changes of the three domains. Then, the measurement method of extension domain change is studied, the cost matrix is constructed, and the optimal granular layer is determined by the minimum cost of extension domain change. The model considers both static and dynamic characteristics comprehensively, and provides a new way to choose the optimal granularity. Finally, taking the data of water resources carrying capacity in Heilongjiang Province as an example, the validity of the model is verified, and the sensitivity analysis is carried out by using classification and regression trees. The results show that the model has good generalization.

Key words: granularity selection, three-way decision, extension set, change cost matrix, water resources carrying capacity

中图分类号:

TP181

李敏,杨亚锋,雷宇,李丽红. 基于可拓域变化代价最小的最优粒度选择[J]. 《山东大学学报(理学版)》, 2021, 56(2): 17-27.

LI Min, YANG Ya-feng, LEI Yu, LI Li-hong. Optimal granularity selection based on minimum cost of extension domain change[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(2): 17-27.

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